Zaha agreed a five-and-a-half-year deal at Old Trafford on January 25, 2013 and was loaned back to Crystal Palace until the summer.
“I am delighted to be joining Manchester United,” said Zaha, who became Sir Alex Ferguson’s final signing as the Scot retired four months later.
“However, my focus for the next five months will be solely at Crystal Palace.
“I have been at Palace for more than 10 years.
“I will always love the club and I want to help get them back to the Premier League, particularly for the fans who have always been so good to me.”
United reportedly agreed a £10million fee up front for the 20-year-old winger, with an extra £5m in additional fees.
Zaha struggled under Ferguson’s successor David Moyes and did not make a single Premier League start for United.
He was loaned to Cardiff in January 2014 before rejoining Palace, first on a temporary deal before signing permanently for the Eagles in February 2015.
The Ivory Coast international has scored 89 goals in 450 Palace appearances.